Hello lostandfound, and welcome to the forum
What's the plan of action here .. do you just want a look at Linux, or a permanent installation ?
If a permanent installation, do you want to keep Windows too ?
is the second HDD an internal drive, or USB ?
If you just want a look, you have a couple of options.
1) Put Live on a CD or USB stick as a LiveCD/LiveUSB
2) Install Ubuntu or Linux Mint "inside" Windows
Both of those have downsides .. but they'll give you a looksee at Linux, and allow you to test drive it without altering your hard drives.
If you want a permanent "proper" Linux installation, where to ? .. the second HDD ?
This would be the best option, but we'd need to work out where's best to put the bootloader .. so we need to know if the second HDD is permanently attached to the PC (as in an internal HDD) or not (as in a USB HDD) ?
Then you need to choose your Linux "Distribution" .. ie. do you go for Ubuntu as it has the largest userbase, or Linux Mint because it's more similar to the Windows interface, or do you want to go for something else .. My advice would be to start with Mint 13 Cinnamon or Ubuntu 12.04 simply because you'll find help and tutorials easier to find, but there are hundreds of other Linux distributions to choose from.
YES there are 64bit versions of most Linux distributions .. certainly the 2 above.
As I said, my advice would be to go for one of those 2 .. added advice would be to first try them BOTH on a LiveUSB, and make up your mind which suits you best before installing to the hard drive.
Be aware, running them from a USB stick will be MUCH slower than running them from a hard drive so don't draw any "speed" conclusions .. but you can check out the interface and see which you like.
Do you want instructions on how to create a LiveUSB stick ?